August Ferdinand Möbius
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August Ferdinand Möbius
August Ferdinand Möbius (, ; ; 17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer. Life and education Möbius was born in Schulpforta, Electorate of Saxony, and was descended on his mother's side from religious reformer Martin Luther. He was home-schooled until he was 13, when he attended the college in Schulpforta in 1803, and studied there, graduating in 1809. He then enrolled at the University of Leipzig, where he studied astronomy under the mathematician and astronomer Karl Mollweide. In 1813, he began to study astronomy under mathematician Carl Friedrich Gauss at the University of Göttingen, while Gauss was the director of the Göttingen Observatory. From there, he went to study with Carl Gauss's instructor, Johann Pfaff, at the University of Halle, where he completed his doctoral thesis ''The occultation of fixed stars'' in 1815. In 1816, he was appointed as Extraordinary Professor to the "chair of astronomy and hi ...
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Adolf Neumann
Friedrich Gustav Adolf Neumann (5 June 1825 – 20 November 1884), was a German painter and engraver. Many of his portraits were published in ''Die Gartenlaube'' and the ''Illustrirte Zeitung''. His brother was the wood engraver . His father worked as a colorist. Although his family was very poor, he gained the approval of Veit Hanns Schnorr von Carolsfeld, who accepted him as his student at the Hochschule für Grafik und Buchkunst Leipzig, Academy of Fine Arts. Later, he worked in the studio of copper engraver Henry Winkles and took lessons from Carl Werner and , who became his friend and supported him after his father's death.Adolf Neumann, from ''Die Gartenlaube''
@ German Wikisource He was best known for his portraits, especially those of musicians, including Franz Schubert, Robert Franz, a ...
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Möbius Transformation
In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form f(z) = \frac of one complex number, complex variable ; here the coefficients , , , are complex numbers satisfying . Geometrically, a Möbius transformation can be obtained by first applying the inverse stereographic projection from the plane to the unit sphere, moving and rotating the sphere to a new location and orientation in space, and then applying a stereographic projection to map from the sphere back to the plane. These transformations preserve angles, map every straight line to a line or circle, and map every circle to a line or circle. The Möbius transformations are the projective transformations of the complex projective line. They form a group (mathematics), group called the Möbius group, which is the projective linear group . Together with its subgroups, it has numerous applications in mathematics and physics. Möbius geometry, Möbius geometries and t ...
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Philology
Philology () is the study of language in Oral tradition, oral and writing, written historical sources. It is the intersection of textual criticism, literary criticism, history, and linguistics with strong ties to etymology. Philology is also defined as the study of literary texts and oral and written records, the establishment of their authentication, authenticity and their original form, and the determination of their meaning. A person who pursues this kind of study is known as a philologist. In older usage, especially British, philology is more general, covering comparative linguistics, comparative and historical linguistics. Classical philology studies classical languages. Classical philology principally originated from the Library of Pergamum and the Library of Alexandria around the fourth century BC, continued by Greeks and Romans throughout the Roman Empire, Roman and Byzantine Empire. It was eventually resumed by European scholars of the Renaissance humanism, Renaissance, ...
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Theodor Möbius
Theodor Möbius (June 22, 1821 Leipzig - April 25, 1890) was a German philologist who specialized in Germanic studies. Biography He was a son of German mathematician August Ferdinand Möbius. He studied at the Universities of Leipzig (1840–42) and Berlin (1842-43), receiving his doctorate in 1844 at Leipzig. From 1845 to 1861, he was an assistant, then later curator, at the university library. He earned his habilitation at Leipzig in 1852 with the thesis ''Über die ältere isländische Saga'', and in 1859 became a professor of Scandinavian languages and literature there. In 1865, he accepted a similar position at Kiel. He edited many old Norse works. Selected works * ''Catalogus librorum islandicorum et norvegicorum ætatis mediæ editorum versorum illustratorum : Skáldatal sive Poetarum recensus Eddæ upsaliensis'', Lipsiæ : Apud W. Engelmannum, 1856. * ''Altnordisches Glossar : wörterbuch zu einer Auswahl alt-isländischer und alt-norwegischer Prosatexte'', Leipzig : B. ...
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Göttingen Observatory
Göttingen Observatory (''Universitätssternwarte Göttingen'' (Göttingen University Observatory) or ''königliche Sternwarte Göttingen'' (Royal Observatory Göttingen)) is a German astronomical observatory located in Göttingen, Lower Saxony, Germany. History In 1802, George III of the United Kingdom, who was also the prince-elector of Hanover, allocated 22,680 thalers for a new observatory. The plans were developed, like many of the university's buildings, by Georg Heinrich Borheck. Construction was delayed by the French Revolutionary Wars and extended from 1803 until 1816. At the time, the building was on the outskirts of Göttingen, to ensure an unobstructed view of the night sky. Carl Friedrich Gauss became the first director of the Observatory, and lived there between 1815 and 1855. Gauss arranged for the installation of two meridian circles (produced by Johann Georg Repsold and Georg Friedrich von Reichenbach in 1818 and 1819. Gauss was succeeded by Wilhelm Weber an ...
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Plume (publisher)
Plume is a publishing company in the United States, founded in 1970 as the trade paperback imprint of New American Library. Today it is a division of Penguin Group Penguin Group is a British trade book publisher and part of Penguin Random House, which is owned by the German media company, media Conglomerate (company), conglomerate Bertelsmann. The new company was created by a Mergers and acquisitions, mer ..., with a backlist of approximately 700 titles. References External links Plume - Penguin Books USA Pearson plc Book publishing companies based in New York (state) Publishing companies established in 1970 {{Publish-corp-stub ...
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Martin Luther
Martin Luther ( ; ; 10 November 1483 – 18 February 1546) was a German priest, Theology, theologian, author, hymnwriter, professor, and former Order of Saint Augustine, Augustinian friar. Luther was the seminal figure of the Reformation, Protestant Reformation, and his theological beliefs form the basis of Lutheranism. He is widely regarded as one of the most influential figures in Western world, Western and History of Christianity, Christian history. Born in Eisleben, Luther was ordained to the Priesthood in the Catholic Church, priesthood in 1507. He came to reject several teachings and practices of the contemporary Catholic Church, Roman Catholic Church, in particular the view on indulgences and papal authority. Luther initiated an international debate on these in works like his ''Ninety-five Theses'', which he authored in 1517. In 1520, Pope Leo X demanded that Luther renounce all of his writings, and when Luther refused to do so, Excommunication in the Catholic Church, ...
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Astronomer
An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galaxies – in either observational astronomy, observational (by analyzing the data) or theoretical astronomy. Examples of topics or fields astronomers study include planetary science, Sun, solar astronomy, the Star formation, origin or stellar evolution, evolution of stars, or the galaxy formation and evolution, formation of galaxies. A related but distinct subject is physical cosmology, which studies the Universe as a whole. Types Astronomers typically fall under either of two main types: observational astronomy, observational and theoretical astronomy, theoretical. Observational astronomers make direct observations of Astronomical object, celestial objects and analyze the data. In contrast, theoretical astronomers create and investigate Con ...
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ...
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Möbius–Kantor Graph
In the mathematics, mathematical field of graph theory, the Möbius–Kantor graph is a symmetric graph, symmetric bipartite graph, bipartite cubic graph with 16 vertices and 24 edges named after August Ferdinand Möbius and Seligmann Kantor. It can be defined as the generalized Petersen graph ''G''(8,3): that is, it is formed by the vertices of an octagon, connected to the vertices of an eight-point star in which each point of the star is connected to the points three steps away from it (an octagram). Möbius–Kantor configuration asked whether there exists a pair of polygons with ''p'' sides each, having the property that the vertices of one polygon lie on the lines through the edges of the other polygon, and vice versa. If so, the vertices and edges of these polygons would form a projective configuration. For ''p'' = 4 there is no solution in the Euclidean plane, but found pairs of polygons of this type, for a generalization of the problem in which the points and edges bel ...
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Möbius–Kantor Configuration
In geometry, the Möbius–Kantor configuration is a configuration consisting of eight points and eight lines, with three points on each line and three lines through each point. It is not possible to draw points and lines having this pattern of incidences in the Euclidean plane, but it is possible in the complex projective plane. Coordinates asked whether there exists a pair of polygons with ''p'' sides each, having the property that the vertices of one polygon lie on the lines through the edges of the other polygon, and vice versa. If so, the vertices and edges of these polygons would form a projective configuration. For p = 4 there is no solution in the Euclidean plane, but found pairs of polygons of this type, for a generalization of the problem in which the points and edges belong to the complex projective plane. That is, in Kantor's solution, the coordinates of the polygon vertices are complex numbers. Kantor's solution for p = 4, a pair of mutually-inscribed quadrilateral ...
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Möbius Configuration
In geometry, the Möbius configuration or Möbius tetrads is a certain configuration in Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are ''Euclidean spaces ... or projective space, consisting of two tetrahedron, tetrahedra that are mutually Inscribed figure, inscribed: each Vertex (geometry), vertex of one tetrahedron lies on a Face (geometry), face plane of the other tetrahedron and vice versa. Thus, for the resulting system of eight points and eight planes, each point lies on four planes (the three planes defining it as a vertex of a tetrahedron and the fourth plane from the other tetrahedron that it lies on), and each plane contains four points (the three tetrahedron vertices of its face, and the vertex from the other tetrahedron that lies on it). Möbius's theorem The configuration ...
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